FactorialNumerals

Factoradic: place $k$ has weight $k!$ and digit at most $k$. The digits of $n$ are the Lehmer code of the $n$-th permutation in lexicographic order, so unranking a permutation and writing a number in this system are the same operation.

FactorialNumerals()the system, place $k$ weighted $k!$

Typed signatures

Type	Package	Applies
() -> value	numerals	always

Domain: Numeral systems

Examples

Basic #

$10 = 1\cdot 3! + 2\cdot 2! + 0\cdot 1!$: the Lehmer code of the 10th permutation

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In$\mathrm{IntegerDigits}(10, \mathrm{FactorialNumerals})$Out$\bigl\lbrack1, 2, 0, 0\bigr\rbrack$

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Examples	1

See also: IntegerDigits, PrimorialNumerals